Second ideal intersection graph of a commutative ring

TL;DR

This paper introduces the second ideal intersection graph for commutative rings, exploring its properties and structure based on the intersection of ideals that are second ideals.

Contribution

It defines and studies the properties of the second ideal intersection graph in commutative rings, a novel concept in algebraic graph theory.

Findings

Characterization of adjacency in SII(R)

Structural properties of the graph related to ring ideals

Conditions for connectivity and completeness

Abstract

Let R be a commutative ring with identity. In this paper, we introduce and investigate the second ideal intersection graph SII(R) of R with vertices are non-zero proper ideals of R and two distinct vertices I and J are adjacent if and only if $I \cap J$ is a second ideal of R.